Analysis of Interval-Valued Intuitionistic Fuzzy Aczel–Alsina Geometric Aggregation Operators and Their Application to Multiple Attribute Decision-Making

Senapati, Tapan; Mesiar, Radko; Šimić, Vladimir; Iampan, Aiyared; Chinram, Ronnason; Ali, Rifaqat

doi:10.3390/axioms11060258

Cited by 42 publications

(21 citation statements)

References 57 publications

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“…Proof. By mathematical induction, we can prove that, Equation (30) holds for all positive integer n. First, we show that Equation (22) holds for n = 2, since…”

Section: Theorem 22mentioning

confidence: 94%

“…Senapati et al introduced the IF Aczel-Alsina weighted averaging (IFAAWA) operator, the IF Aczel-Alsina orders weighted averaging (IFAAOWA) operator, and the IF Aczel-Alsina hybrid averaging (IFAAHA) operator. Senapati et al [29,30] developed interval-valued intuitionistic fuzzy aggregation operators, such as the IVIF Aczel-Alsina weighted averaging/geometric operator, the IVIF Aczel-Alsina order weighted averaging/geometric operator, and the IVIF Aczel-Alsina hybrid averaging/geometric operator and built up several features of such operators. Senapati [31] also defined picture fuzzy aggregation operator such as the PF Aczel-Alsina weighted average (PFAAWA) operator, the PF Aczel-Alsina order weighted average (PFAAOWA) operator, and the PF Aczel-Alsina hybrid average (PFAAHA) operator with their properties.…”

Section: Introductionmentioning

confidence: 99%

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A Novel Approach on Decision Support System Based on the Aczel-Alsina Aggregation Operators and Their Applications to Supplier Selection Problems

Wang¹,

Bonyah²,

Khayyat

et al. 2022

Journal of Function Spaces

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Induced aggregation operators are more suitable for aggregating the individual preference relations into a collective fuzzy preference relation. Therefore, in this paper, we introduce the notion of some new types of induced aggregation operators, based on the Aczel-Alsina operations. We construct some induced interval-valued intuitionistic trapezoidal fuzzy Aczel-Alsina ordered weighted averaging/geometric (I-IVITrFAAOWA/G) operator, induced interval-valued intuitionistic trapezoidal fuzzy Aczel-Alsina hybrid averaging/geometric (I-IVITrFAAHA/G) operator. Moreover, some dominant properties of these developed operators are studied in detail. Based on these proposed approaches, a model is a build up for multicriteria decision making (MCDM), and their stepwise algorithm is being presented. Finally, in utilizing the developed approach, an illustrative example is solved with the help of proposed operators. In the end, we utilize an applicable example for supplier selection to prove the proposed methods and compare the result with existing methods, which shows the superiority, competence, and ability of the developed model.

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“…Proof. By mathematical induction, we can prove that, Equation (30) holds for all positive integer n. First, we show that Equation (22) holds for n = 2, since…”

Section: Theorem 22mentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

A Novel Approach on Decision Support System Based on the Aczel-Alsina Aggregation Operators and Their Applications to Supplier Selection Problems

Wang¹,

Bonyah²,

Khayyat

et al. 2022

Journal of Function Spaces

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“…Based on the Aczel-Alsina triangular norm (AA t-norm), Wang et al [49] devised a score level hybrid method. In recent times, Senapati et al [42][43][44][45] have developed ''(interval-valued) intuitionistic fuzzy Aczel-Alsina aggregation operators'' and implemented them to MADM technique.…”

Section: Research Gap and Motivation Of The Studymentioning

confidence: 99%

Selection of Appropriate Global Partner for Companies Using q-Rung Orthopair Fuzzy Aczel–Alsina Average Aggregation Operators

Senapati

Martínez

Chen

2022

Int. J. Fuzzy Syst.

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The term “q-Rung orthopair fuzzy sets ($$q^{r}$$ q r OFSs)” refers to the collection of the most differentiated ideas for expressing fuzzy data in decision-making rules. The $$q^{r}$$ q r OFSs can gradually adapt the region of information by adjusting the parameter $$q \ge 1$$ q ≥ 1 in response to the fluctuation degree, so assisting in the generation of more numerous possibilities. Aczel–Alsina triangular norm and conorm are superior operations that may create general and adaptable working principles for aggregating arguments. To make use of $$q^{r}$$ q r OFSs and Aczel–Alsina triangular norms in “multiple attribute decision-making (MADM)” issues, a few q-rung orthopair fuzzy ($$q^{r}$$ q r OF) Aczel–Alsina aggregation operators: $$q^{r}$$ q r OF Aczel–Alsina weighted average ($$q^{r}$$ q r OFAAWA) operator, $$q^{r}$$ q r OF Aczel–Alsina order weighted average ($$q^{r}$$ q r OFAAOWA) operator, $$q^{r}$$ q r OF Aczel–Alsina hybrid average ($$q^{r}$$ q r OFAAHA) operator for aggregating $$q^{r}$$ q r OFSs are exhibited in this article to fix the MADM issues based on $$q^{r}$$ q r OFSs. Some significant properties are additionally demonstrated. A technique for taking care of the MADM issues is proposed based on these created operators. The adequacy of the suggested technique is shown by means of a numerical example on enterprise partner selection, a lot of investigations and correlations with other existing strategies. The sensitivity of the proposed aggregation operators to decision-making findings is investigated. The demonstration outcomes suggest that the suggested technique has fulfilling universality and adaptability in aggregating $$q^{r}$$ q r OF data and acquiring the correlations of criteria and the attitudes of “decision-makers (DMs)” and is doable and compelling for taking care of the MADM issues dependent on $$q^{r}$$ q r OFSs.

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“…Many researchers used AAΤΝ and ΤCΝ and concluded that these norms and conorms give better results due to their parameters. Senapati et al [23][24][25][26][27][28][29][30] recognized the IF, IVIF, HF, PF, IVPF, and linguistic IF aggregation operators based on the AA-ΤΝ and AA-ΤCΝ by using the MADM challenges. Hussain et al [31] used the AA aggregation operators on TSFSs.…”

Section: Research Gap and Motivation Of The Study Atanassovmentioning

confidence: 99%

A Novel SIR Approach to Closeness Coefficient‐Based MAGDM Problems Using Pythagorean Fuzzy Aczel–Alsina Aggregation Operators for Investment Policy

Haq

Shaheen

Ali

et al. 2022

Discrete Dynamics in Nature and Society

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In this study, a novel Pythagorean fuzzy aggregation operator is presented by combining the concepts of Aczel–Alsina ( A A ) T-norm and T-conorm operations for multiple attribute group decision-making (MAGDM) challenge for the superiority and inferiority ranking (SIR) approach. This approach has many advantages in solving real-life problems. In this study, the superiority and inferiority ranking method is illustrated and showed the effectiveness for decision makers by using multicriteria. The Aczel–Alsina aggregation operators on interval-valued IFSs, hesitant fuzzy sets (HFSs), Pythagorean fuzzy sets (PFSs), and T-spherical fuzzy sets (TSFSs) for multiple attribute decision-making (MADM) issues have been proposed in the literature. In addition, we propose a Pythagorean fuzzy Aczel–Alsina weighted average closeness coefficient ( PF − A A − WA − C C ) aggregation operator on the basis of the closeness coefficient for MAGDM challenges. To highlight the relevancy and authenticity of this approach and measure its validity, we conducted a comparative analysis with the method already in vogue.

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Analysis of Interval-Valued Intuitionistic Fuzzy Aczel–Alsina Geometric Aggregation Operators and Their Application to Multiple Attribute Decision-Making

Cited by 42 publications

References 57 publications

A Novel Approach on Decision Support System Based on the Aczel-Alsina Aggregation Operators and Their Applications to Supplier Selection Problems

A Novel Approach on Decision Support System Based on the Aczel-Alsina Aggregation Operators and Their Applications to Supplier Selection Problems

Selection of Appropriate Global Partner for Companies Using q-Rung Orthopair Fuzzy Aczel–Alsina Average Aggregation Operators

A Novel SIR Approach to Closeness Coefficient‐Based MAGDM Problems Using Pythagorean Fuzzy Aczel–Alsina Aggregation Operators for Investment Policy

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